Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2881 : Algebra Ii

What is the value of ?

Possible Answers:

Correct answer:

Explanation:

A factorial represents the product of all natural numbers less than a given number. Thus, 4! = 4*3*2*1 which gives us .

Report an Error

Example Question #3 : Other Factorials

Solve the Quadratic Equation.

4x^2 = 12x - 5

Possible Answers:

2/5, 2

3/4, 1/2

1, 1

5/2, 2/5

{5/2, 1/2}

Correct answer:

{5/2, 1/2}

Explanation:

First, move all terms to the left by subtracting the quantity on the right.

$4x^{2} = 12x - 5$

-(12x - 5) -(12x - 5) = 0

$= 4x^{2} - 12x + 5 = 0$

From here, factor the quadractic into two binomials and set each equal to zero.

= (2x - 5) (2x - 1)

2x - 5 = 0

+ 5 + 5

2x = 5

x = 5/2

2x - 1 = 0

+1 +1

2x = 1

x = 1/2

Report an Error

Example Question #5 : Other Factorials

What is $\frac{10!}{7!}$ ?

Possible Answers:

720

810

4305

Correct answer:

720

Explanation:

Remember that factorial is defined as:

$n! = n \cdot (n-1)\cdot (n-2) \cdots \cdot (3)\cdot (2)\cdot (1)$

So using this definition, 10! = 10*9*8*7*6*5*4*3*2*1

And 7! = 7*6*5*4*3*2*1 .

So $\frac{10!}{7!} = \frac{10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}$

The 7, 6, 5, 4, 3, 2, and 1 all cancel from both the numerator and denominator. So we're left with just 10*9*8 on top, which has a value of 720 .

Report an Error

Example Question #1 : Other Factorials

How many -permutations (without repetition) are there when taking numbers from the set of numbers $\begin{Bmatrix} 16, 11, 9, 7, 14, 12, 18, 23, 1 \end{Bmatrix}$ ?

Possible Answers:

729

504

3024

Correct answer:

504

Explanation:

The elements of the set don't matter. Only the size of the set matters when determining permutations.

Our set contains 9 integers, so for the first number in our permutation, we have 9 choices.

After picking that number, because we're not allowed repetition, our second number is from 8 choices.

Our final number is from 7 choices.

Multiplying 9*8*7 gives us 504 .

Report an Error

Example Question #77 : Factorials

What can n!(n+1) be expressed as?

Possible Answers:

n(n+1)

(n+1)!

n(n+1)!

n+1

Correct answer:

(n+1)!

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach . Since we are dealing with variables, let's analyze them. n+1 is definitely greater than in this situation because factorials are always positive numbers. If we took the difference between n+1 and we would get . This means after , the next biggest value is n+1 . Since we have and the next value multiplied is n+1 , we can conclude that (n+1)! will work since it incorporates values multiplied and also n+1 .

Report an Error

Example Question #5 : Other Factorials

What is ?

Possible Answers:

Correct answer:

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach .

So, is $3\cdot 2\cdot 1$ .

Multiplying that out, we get .

Report an Error

Example Question #9 : Other Factorials

What is ?

Possible Answers:

120

100

Correct answer:

120

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach .

So, is $5\cdot 4\cdot 3\cdot 2\cdot 1$ .

Multiplying that out, we get 120 .

Report an Error

Example Question #10 : Other Factorials

What is $3! \cdot 4!$ ?

Possible Answers:

5040

144

256

Correct answer:

144

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach .

So, is $3\cdot 2\cdot 1$ . Multiplying that out, we get .

We also have . That is $4\cdot 3\cdot 2\cdot 1$ or .

Since we are multiplying the factorial, we multiply and to get 144 .

Report an Error

Example Question #11 : Other Factorials

What is $\frac{6!}{4!}$ ?

Possible Answers:

$\frac{6}{5}$

Correct answer:

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach .

So, is $6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1$ . We also have . That is $4\cdot 3\cdot 2\cdot1$ .

Since we are dividing the factorial, we can cancel out some terms.

Both the numerator and denominator have $4\cdot 3\cdot 2\cdot 1$ , and we can cancel those out. We are left with $6\cdot 5$ or 30.

Report an Error

Example Question #81 : Factorials

What is $\frac{7!}{30}$ ?

Possible Answers:

168

$\frac{1}{168}$

$\frac{1}{7}$

Correct answer:

168

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach .

So, is $7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1$ . We are dividing by 30. With careful inspection, can be broken down to $6\cdot5$ .

If we cancel that out with the ones in the numerator, we have $7\cdot 4\cdot 3\cdot 2\cdot 1$ or 168 .

Report an Error

View Algebra 2 Tutors

Matthew
Certified Tutor

Bluffton University, Bachelor of Education, Mathematics. Bluffton University, Masters in Education, Education.

View Algebra 2 Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View Algebra 2 Tutors

Kara
Certified Tutor

University of Central Missouri, Bachelor of Science, Science Teacher Education. University of Central Missouri, Certificate, ...

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

LSAT Tutors in San Francisco-Bay Area, SAT Tutors in Houston, Chemistry Tutors in Houston, Physics Tutors in Houston, Algebra Tutors in Washington DC, SSAT Tutors in San Diego, ACT Tutors in Dallas Fort Worth, Algebra Tutors in Chicago, English Tutors in Denver, Computer Science Tutors in San Francisco-Bay Area

Popular Courses & Classes

ACT Courses & Classes in Philadelphia, MCAT Courses & Classes in Miami, SAT Courses & Classes in Denver, MCAT Courses & Classes in San Diego, MCAT Courses & Classes in Boston, GMAT Courses & Classes in Denver, ISEE Courses & Classes in Denver, LSAT Courses & Classes in San Diego, SAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Seattle

Popular Test Prep

MCAT Test Prep in Washington DC, GMAT Test Prep in Denver, ISEE Test Prep in San Francisco-Bay Area, LSAT Test Prep in San Diego, ACT Test Prep in Philadelphia, SSAT Test Prep in Washington DC, LSAT Test Prep in Los Angeles, GRE Test Prep in Boston, SAT Test Prep in San Diego, LSAT Test Prep in Seattle

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #2881 : Algebra Ii

Example Question #3 : Other Factorials

Example Question #5 : Other Factorials

Example Question #1 : Other Factorials

Example Question #77 : Factorials

Example Question #5 : Other Factorials

Example Question #9 : Other Factorials

Example Question #10 : Other Factorials

Example Question #11 : Other Factorials

Example Question #81 : Factorials

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: